Problem: Solve for $x$ and $y$ using substitution. ${-2x-3y = 0}$ ${x = y-5}$
Answer: Since $x$ has already been solved for, substitute $y-5$ for $x$ in the first equation. ${-2}{(y-5)}{- 3y = 0}$ Simplify and solve for $y$ $-2y+10 - 3y = 0$ $-5y+10 = 0$ $-5y+10{-10} = 0{-10}$ $-5y = -10$ $\dfrac{-5y}{{-5}} = \dfrac{-10}{{-5}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = y-5}\thinspace$ to find $x$ ${x = }{(2)}{ - 5}$ ${x = -3}$ You can also plug ${y = 2}$ into $\thinspace {-2x-3y = 0}\thinspace$ and get the same answer for $x$ : ${-2x - 3}{(2)}{= 0}$ ${x = -3}$